The changes look fairly straight forward or reasonable to me.
Support data ownership in uiSearchItems sounds reasonable as well, but I haven't looked into the details of that.

[...] or to adjust the exec callback so it just gets the UI string, not a pointer to the item. Ideally the search wouldn't get any pointers at all, I suppose. That seems like a bigger change though, so I'd like to get feedback on this first.

The string will not be enough since you can have multiple search results with the same string. E.g. linked data-blocks with the same name, or overriden data-blocks (where the source data-block and the override version of it always have the same name). That's why the pointer is used, but for IDs it would in fact be nicer to use the ID.session_uuid instead.
In a better design you could completely customize how you match items.

For a quick/simple fix you could store what kind of data type the uiSearchItems.pointers contain and do comparisons based on that. Say a uiSearchItems.pointer_type enum. E.g. if string comparison is good enough, the pointer type can be string and UI code does string comparisons. Or maybe best in this case, you use a session UUID as pointer type.